A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of (3v^(2))/(4g) with respect to the initial position . The object is

A small object of uniform density rolls up a curved surface with an in

1.	A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of (3v^(2))/(4g) with respect to the initial position . The object is
Answer» hollowsphere DISC ring solid sphere Solution :The kinetic ENERGY of the rolling object is converted into potential energy at height `h (= (3v^2)/(4G))` So by the LAW of conservation of mechanical energy , we have `(1)/(2) mv^(2) + (1)/(2) I omega^(2) = Mgh` `(1)/(2) Mv^(2) + (1)/(2) I ((V)/(R))^(2) = Mg ((3v^2)/(4g)) (because omega = (v)/(R))` `(1)/(2) I (v^(2))/(R^(2)) = (3)/(4) Mv^(2) - (1)/(2) Mv^(2) , or I = (1)/(2) MR^(2)` Hence the object is disc.